Example

If an activity has optimistic duration 6 days, pessimistic duration 4 days and most likely duration 5 days then the expected duration is equal to 5 days.

ES – Early Start time,  EF – Early Finish time

LS – Late Start time , LF – Late Finish time

Slack=LS-ES or Slack=LF-EF

Activities: A, B, C, D, E

Start date = date 0

Duration A = 12 days, Duration B = 10 days, Duration C = 10 days, Duration D = 5 days, Duration E = 3 days

Activities D and E go to FINISH. The time to complete the project is the highest of the EF times of the Predecessor nodes i.e. activities D and E cannot be completed in longer than 27 days. LF(E)=27.

ES(A)=0, EF(A)=12

LS(A)=0, LF(A)=12

ES(B)=0, EF(B)=10

LS(B)=2, LF(B)=12

ES(D)=22, EF(D)=27

LS(D)=22, LF(D)=27

ES(E)=22, EF(E)=25

Forward Pass: ES(C)=EF of Predecessor activities (largest)=12, EF(C)=ES+Duration of the activity=12+10=22

Backward Pass: LS(E)=27-3=24, LF(C)=LS of Successor activities (smallest)=22, LS(C)=LF- Duration=22-10=12

Slack(A)=0, Slack(B)=2, Slack(C)=0, Slack(D)=0, Slack (E)=2

Slack is the time an activity can be delayed without causing another activity to be delayed or impacting the completion date of the project.

The Critical Path is ACD.